Damping devices of this type are prior art. Such hydraulic dampers, also called noise dampers or silencers, are used to reduce the vibrations generated by pressure pulsations. Pressure pulsations are periodically imparted to a related hydraulic system, in particular, as a result of the operation of the hydraulic pumps. As shown in DE 102 17 080 C1, the known damping devices of this kind have a damping housing in the form of a circular cylinder, which is spherically rounded at both axial end sections. A fluid inlet and a fluid outlet are situated at each end section coaxially to the cylindrical axis. In these damping devices, the damping chamber, which the fluid flow traverses from the fluid inlet to the fluid outlet, is provided in the form of a damping tube. The damping tube extends coaxially between the fluid inlet and the fluid outlet, and includes openings in the tube wall to the fluid chamber surrounding the tube. The fluid chamber, in conformity with the cylinder diameter, is expanded radially relative to the axial through-flow direction predefined by the damping tube.